A258788
a(n) = [x^n] Product_{k=1..n} 1/(x^k*(1-x^k)).
Original entry on oeis.org
1, 1, 3, 12, 47, 192, 811, 3539, 15765, 71362, 327748, 1524081, 7161629, 33958506, 162312471, 781305581, 3784573140, 18435578714, 90261022638, 443956543235, 2192796266004, 10872208762458, 54095648185434, 270029668955605, 1351943521270155, 6787479872751732
Offset: 0
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T:=proc(n, k) option remember; `if`(n=0 or k=1, 1, T(n, k-1) + `if`(n
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Table[SeriesCoefficient[1/Product[x^k*(1-x^k), {k, 1, n}], {x, 0, n}], {n, 0, 30}]
Table[SeriesCoefficient[1/Product[1-x^k, {k, 1, n}], {x, 0, n*(n+3)/2}], {n, 0, 30}]
A258798
a(n) = [x^n] Product_{k=1..n} (1+x^k)^3 / x^k.
Original entry on oeis.org
1, 3, 12, 62, 327, 1851, 10802, 64440, 391218, 2408001, 14989608, 94197594, 596756374, 3807010920, 24435261432, 157681777148, 1022391454116, 6657413851086, 43517229086467, 285447137446989, 1878287880309900, 12395149957521672, 82014499806039711
Offset: 0
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Table[SeriesCoefficient[Product[(1+x^k)^3/x^k, {k, 1, n}], {x, 0, n}], {n, 0, 30}]
Table[SeriesCoefficient[Product[1+x^k, {k, 1, n}]^3, {x, 0, n*(n+3)/2}], {n, 0, 30}]
(* A program to compute the constant d *) (1+r)^3/r^2 /.FindRoot[-Pi^2/12 - Log[r]^2/3 + 1/2*Log[1+r]^2 + PolyLog[2,1/(1+r)] == 0, {r, E}, WorkingPrecision->100]
A258799
a(n) = [x^n] Product_{k=1..n} (1+x^k)^3 / x^(2*k).
Original entry on oeis.org
1, 1, 3, 13, 61, 324, 1800, 10340, 60969, 366486, 2237120, 13829487, 86394782, 544547651, 3458637273, 22113504345, 142212705879, 919294844898, 5969839457411, 38927450022860, 254776529381625, 1673102335692514, 11020847332241873, 72798664086854460
Offset: 0
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Table[SeriesCoefficient[Product[(1+x^k)^3/x^(2*k), {k, 1, n}], {x, 0, n}], {n, 0, 30}]
Table[SeriesCoefficient[Product[1+x^k, {k, 1, n}]^3, {x, 0, n*(n+2)}], {n, 0, 30}]
(* A program to compute the constant d *) (1+r)^3/r /.FindRoot[Log[1+r]/Log[r] + (PolyLog[2,-r] + Pi^2/12) / Log[r]^2 == 1/6, {r, E}, WorkingPrecision->100]
Showing 1-3 of 3 results.